JAMB Mathematics Past Questions & Answers - Page 287

1,431.

Two perpendicular lines PQ and QR intersect at (1, -1). If the equation of PQ is x - 2y + 4 = 0, find the equation of QR

A.

x + 2y - 1= -0

B.

2x + y - 3 = 0

C.

x - 2y - 3 = 0

D.

2x + y - 1 = 0

Correct answer is D

Line PQ : x - 2y + 4 = 0

2y = x + 4 \(\implies y = \frac{x}{2} + 2 \)

Slope = \(\frac{1}{2}\)

Slope of the perpendicular line QR: \(\frac{-1}{\frac{1}{2}} = -2\)

Line QR: \(y = mx + b\)

\(y = -2x + b\) 

Point of intersection: (1, -1)

\(-1 = -2(1) + b \implies b = -1 + 2 = 1\)

\(y = -2x + 1 \implies y + 2x - 1 = 0\)

\(QR: 2x + y - 1 = 0\)

1,432.

Find the distance between two towns P(45°N, 30°W) and Q(15°S, 30°W) if the radius of the earth is 7000km. [\(\pi = \frac{22}{7}\)]

A.

\(\frac{1100}{3}\)km

B.

\(\frac{2200}{3}\)km

C.

\(\frac{22000}{3}\)km

D.

\(\frac{1100}{3}\)km

Correct answer is C

Angular difference = 45° + 15° = 60°.

\(D = \frac{60°}{360°} \times 2 \times \frac{22}{7} \times 7000\)

= \(\frac{22000}{3} km\)

1,433.
1,434.

If x = \(\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\) and y = \(\begin{pmatrix} 2 & 1 \\ 4 & 3 \end{pmatrix}\). Find xy.

A.

\(\begin{pmatrix} 10 & 7 \\ 12 & 9 \end{pmatrix}\)

B.

\(\begin{pmatrix} 2 & 7 \\ 4 & 17 \end{pmatrix}\)

C.

\(\begin{pmatrix} 10 & 4 \\ 4 & 6 \end{pmatrix}\)

D.

\(\begin{pmatrix} 4 & 3 \\ 10 & 9 \end{pmatrix}\)

Correct answer is A

\(\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\); y = \(\begin{pmatrix} 2 & 1 \\ 4 & 3 \end{pmatrix}\).

= \(\begin{pmatrix} 2 + 8 & 1 + 6 \\ 0 + 12 & 0 + 9 \end{pmatrix}\)

= \(\begin{pmatrix} 10 & 7 \\ 12 & 9 \end{pmatrix}\)

1,435.

\(\begin{vmatrix} -2 & 1 & 1 \\ 2 & 1 & k \\1 & 3 & -1 \end{vmatrix}\) = 23

A.

1

B.

2

C.

3

D.

4

Correct answer is B

-2(-1 - 3k) - 1(-2 -k) + 1(6 - 1) = 23

7k = 14

k = 2